Euler's Gem: The Polyhedron Formula and the Birth of Topology

Portada
Princeton University Press, 15 d’abr. 2012 - 317 pàgines

Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.


From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.


Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

 

Què opinen els usuaris - Escriviu una ressenya

LibraryThing Review

Revisió d'Usuari  - ztutz - LibraryThing

This book is a very well written and easy to read introduction to why topology exists. The central theme of the book is Euler's polyhedron formula, which is so simple that anyone who knows how to ... Llegeix la ressenya completa

Continguts

Introduction
1
chapter1
10
chapter2
27
chapter3
31
chapter4
36
chapter5
44
chapter6
51
chapter7
63
chapter17
173
chapter18
186
chapter19
202
chapter20
219
chapter21
231
chapter22
241
chapter23
253
epilogue
265

chapter8
75
chapter9
81
chapter10
87
chapter11
100
chapter12
112
chapter13
119
chapter14
130
chapter15
145
chapter16
156
ack
271
AppendixA
273
AppendixB
283
Notes
287
illcredits
295
references
297
index
311
Copyright

Altres edicions - Mostra-ho tot

Frases i termes més freqüents

Sobre l'autor (2012)

David S. Richeson is associate professor of mathematics at Dickinson College.

Informació bibliogràfica